In 1968 Dixmier gave an example [1]} of BC solution: he showed that for any complex number \(\alpha \)  in \({\bf C}\)  the differential operators
\(L=H^2+2x\qquad \text{and} \qquad B=H^3+\frac{3}{2}(xH+Hx),\qquad \mbox{with} \quad H={\partial ^2+x^3+\alpha }\) 
